In response to the refusal of most Chinese Catholics to accept the CPA, the CCP engaged in numerous acts of persecution against leaders and members of the "underground" church. Persecution of Catholics was especially severe during the so-called Cultural Revolution of the 1960s, when the CCP adopted a policy of eliminating religion altogether, rather than merely controlling it. That policy was essentially abandoned by the late 1970s, but persecution of the "underground" church continued.
In more recent years, however, there have been efforts to overcome the conflict between the CCP and the RCC. Most notably, in 2018, an agreement was struck between the Vatican and Beijing. Under the terms of the agreement, the CCP plays a role in the appointment of Catholic bishops, but the Pope retains the final say over appointments. In addition, it was agreed that both sides would recognize the Pope as the supreme leader of all Catholics. Needless to say, the agreement, which is up for renewal soon, has been controversial. Some have seen it as a sellout to the CCP; others, like Pope Francis himself, have defended it as a means of maintaining the church's existence in China and limiting the persecution of Catholic believers in China.
However, regardless of how one views the current rapprochement between the Vatican and Beijing, what cannot be argued is that the CCP's attempts to control the activities of the RCC in China have historical precedents. Confronted by the efforts of Catholic missionaries to spread their faith in China, past rulers of the country also tried to limit the spread of Catholicism through various restrictions. For example, during the reign of the Kangxi (K'ang-Hsi) emperor (1661-1722) of the Qing Dynasty (1644-1911), Catholic missionaries were required to obtain government-issued certificates to preach. In addition, the emperor instituted further measures, as he tells us in his own writings:
Since I discovered on the Southern Tour of 1703 that there were missionaries wandering at will over China, I had grown cautious and determined to control them more tightly: to bunch them in larger cities and in groups that included men from several different countries, to catalogue their names and residences, and to permit no new [religious] establishments without my express permission. (as quoted by Jonathan D. Spence in Emperor of China: Self-Portrait of K'ang-Hsi, p. 81).
The emperor even went so far as to attempt to define Catholic teaching (something the CCP appears to be doing as well through its policy of "sinicization," see this report). During the 17th and 18th centuries, Catholic missionaries in China disagreed among themselves over the question of whether Chinese converts could participate in traditional rites honoring ancestors and the ancient philosopher Confucius. Missionaries of the Jesuit order argued that they could since these ceremonies were not actually religious in nature; other Catholic missionaries rejected this view. In the end, the emperor himself intervened. As historian Jonathan Spence explains: "[Kangxi] told the Jesuits and other missionaries that they would be allowed to stay on in China only if they signed certificates stating that they understood and agreed with the definition of Confucian and ancestral rituals which [Kangxi himself] had formulated. Those refusing to sign were deported" (Emperor of China: Self-Portrait of K'ang-Hsi, p. xix). Moreover, to further assert his authority over the activities of the Catholic missionaries in China, the emperor rejected the proposed stationing of a papal emissary in Beijing. (As it would turn out, the emperor's attempted resolution of the "Rites Controversy" would not be the final word; a number of years later, the Pope would rule that Chinese Catholics could not participate in ancestral rites.)
In short, in attempting to bring Catholicism in China under strict government control, the CCP is simply following in the footsteps of previous rulers of the country. However, given the persistence of the Catholic faith in China, it seems likely that whatever policies the CCP adopts toward the RCC, they will be of limited effectiveness.
Image: Picture of Catholic church in Qingdao, China from Wikimedia Commons